The broad long-term objectives of this proposal are to extend and refine the statistical models and methods used in mapping genes and testing for linkage, and to develop new ones where appropriate. In addition we hoe to develop sound statistically-based procedures for integrating a wide variety of map data which throws light on the position of genetic loci along chromosomes. The specific aims of the proposal fall into four broad areas: A) Extensions and applications of the Chi-square model for crossovers; B) Further development of the No Chromatid Interference model for crossovers; C) Integration of gene maps; and D) Statistical models for recombination in fungi. Under A) we propose to derive algorithms permitting the use of the Chi- square model with human pedigree data and with single sperm data, including an allowance for genotyping errors; to study the asymptotic behavior of the model, and its robustness to model misspecification and model error; and to study the variation in recombination rates and in the pattern of interference between arms within an organism, and between organisms. Under B) we propose to compare and contrast the No Chromatid Interference model and the Poisson (No Interference) model for multilocus recombination under a variety of conditions involving incomplete data, such as incomplete penetrance, unknown phase and missing data, with interest focussing on the relative efficiencies of theses models for ordering loci and estimating recombination fractions, and their relative robustness to genotyping errors. For area C) we propose to develop a workable and statistically sound method for summarizing linkage maps, including summary statements of uncertainty; statistical procedures for integrating (combining) linkage maps from different studies, and for integrating linkage maps with other types of maps such as physical or radiation hybrid maps. Finally, under D) we plan to construct a range of biologically-inspired stoichastic models for recombination in fungi which are applicable to multiple loci, and to both reciprocal (crossing over) and non-reciprocal (gene conversion) events. These models will be used to analyze a number of large fungal data sets in which both forms of recombination occur, with the aim of rigorously testing the biological assumptions embodied in the models. To achieve these aims we plan to make the fullest possible use of existing statistical theory and methods, to develop new theory or methods as required, and to take full advantage of the freedom bestowed upon modern statisticians by cheap high-speed computing.